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Relaxed excited states of Tl+—Like centers in alkali halides, polarization effect of Ga+ center
Journal of Luminescence 18/19 (1979) 33 1—335 © North-Holland Publishing Company
RELAXED EXCITED STATES OF TI—LIKE CENTERS IN ALKALI HALIDES, POLARIZATION EFFECT OF Ga~CENTER LE SI DANG, Y. MERLE D’AUBIGNE and R. ROMESTAIN Laboratoire de Spectrométrie Physique.* Universifé Scienrifique et Médicale de Grenoble, 38041 Grenoble-Cedex, France
The linear polarization of the AT emission is another clue to the symmetry of the
3T
1, excited states. Besides, it yields quantitative information about dynamical processes such as feeding rates and relaxation or tunneling between the different sublevels ~
1. Introduction Titlike ions in alkali halides have been studied for many years. Measurements of the polarization of the emitted light, when the crystal is excited with polarized light, have shown that the so called A1 emission originates in an orbital triplet with tetragonal Jahn—Teller distortions. Such a study was carried out in KBr:Ga~ at 4.2K by Fukuda et al. [1]. We have measured the temperature dependence of this polarization. The exact level structure of KBr:Ga~being known from EPR [2], it was possible to make a detailed analysis of this temperature dependence. Such quantities as: (i) the populating rates of the various Jahn—Teller wells when exciting with polarized light, (ii) the relaxation times between the various spin sublevels, could be deduced from this analysis. We will briefly recall the model describing the Jahn—Teller effect in the relaxed excited states of Ga~in KBr, then describe the experimental arrangement we used. In the last section we will make the analysis of the temperature dependence of the linear polarization observed. 3T The AT emission from In transitions between the 1~relaxed excited 1Aig originates ground state. the present experiment it is excited by states and the in the A absorption band, ‘Aig~~3Tiu.Optical detection of EPR pumping directly has shown that the 3T 1~excited states are strongly coupled to Eg vibrational modes and this results in static, tetragonal Jahn—Teller distortions [2, 3]. The Jahn—Teller energy is much larger than the spin—orbit coupling constant so that the quantum number J = L + S loses its significance and the level structure is as indicated in fig. 1 (a similar situation would hold for the In~ion but for Tl~the spin—orbit coupling is very large and J keeps its significance). The system lies in one of the Jahn—Teller wells 3T shown in fig. 1. Each of these corresponds to a particular orbital state of the 1~level which we label X, Y and Z. Similarly we *~boratoire associé au C.N.R.S. 331
I e Si Dang ci al/Relaxed excited states of El 1 2 3 1 ~
like cenlers
2)
~(i+~
(1_2~)~2 i—~
2
2
~
x~
John -Teller 1 1 r 1 distortion L100J L°10J Orbital state Y Fig. I. Level structure and optical selection rules of the A
~
[001 Z
1 relaxed excited states of Ga center Wavy arrows indicates the feedings of various spin sublevels for an excitation light polarized along the [1001 direction
label x, y, z the spin triplet states. Dipole—dipole interaction and second order effect of the spin—orbit coupling partially lift the spin degeneracy as shown in fig. I. For a [100] distortion, the singlet Xx state is the lowest and optical transitions from this state to the ground state are strictly forbidden. The doublet states X~ and Xz emit light polarized along the Z and Y directions, respectively. These selection rules are deduced from the fact that the wavefunction (Xy Yx) transforms like the z component of the T1~representation of the Oh group. It is interesting to note that a center which is distorted along a given tetragonal direction emits light polarized in the plane perpendicular to this direction. These selection rules were carefully checked in various cases of strong Jahn—Teller coupling [2,4]. In the case of strong spin—orbit coupling J is a good quantum number and the simple selection rule remains true: the center emits light polarized along the direction of the Jahn—Teller distortion. In NaCl:Ga~the two radiative states, say Xy and Xz for the X distortion, are effectively degenerate [3]. In KBr:Ga they are split by 2E 16GHz which remain small with respect to the zero field splitting D 93.6 GHz between the singlet and the doublet [21. The origin of this orthorhombic term E in the spin-Hamiltonian is not clear: impurity or off-center effect... Since E can he positive or negative, one obtains two non-equivalent centers for each tetragonal Jahn—Teller distortion. 2. Experimental results The measurements made at 4.2 K are in excellent agreement with those of Fukuda et al. [11. We will only describe those made in a simple geometry: both the exciting beam and the collected beam of emitted light propagate along a 10011 direction of the crystal. One defines the polarization factor as P (iii I )/(Iii+ I ), where ~ and I are the intensity of the emitted light with
Le Si Dang et al./ Relaxed excited states of Tl~-likecenters
Temperature
133
(K )
Fig. 2. Temperature dependence of the polarization factor P of the AT emission for polarized excitation at 4.4eV: open circles are experimental points, solid line is theory (see text). Inset shows the variation of the polarization factor when exciting with polarized light in different parts of the A (4.6 eV) and B (4.75 eV) absorption bands at T 4.2 K.
polarization respectively parallel and perpendicular to the polarization of the excitation light. As expected the polarization factor P is maximum when the polarization of the exciting light is along the [100] or [010] directions of the crystal and is zero for the [1101 direction. As shown in the inset of fig. 2 the polarization factor depends on the wavelength of the excitation light. The measurements of the temperature dependence of P are made for low energy excitation as indicated by an arrow in the A absorption band where the effect is the largest. As shown in fig. 2 the effect of temperature on the polarization factor is large. At very low temperatures the relaxation mechanisms are not very efficient so the polarization reflects the feeding rates of the various orbital and spin states. The measurements could not be made above 50 K since most of the emitted light goes into the A~band [5]. It is clear that in this temperature range the polarization factor tends to saturate at a value different from zero. This shows that only relaxation inside a given well takes place because tunneling from one Jahn—Teller well to another would lead to a complete depolarization of the emitted light. Such depolarization is indeed observed for In~in various alkali halides [61for which it is still possible to observe the AT emission at temperatures as high as 300 K.
3. Quantitative analysis of the polarization We will analyse the polarization obtained when pumping with light polarized along the X direction. First let us assume there is no depolarizing effect. Then transitions in the A band are allowed toward the Yz and Zy states. If there were no relaxation, emission would take place from these same states and thus would
114
Le Si Dang ci al/Relaxed excited states of T!’-like centers
be fully X polarized. Relaxation takes place inside a given well and at high temperature will tend to equalize the population of the two radiative levels. Emission occurs now from Yz, Yx, Zy and Zx states which emit X, Z, X and Y polarized light, respectively. Then the polarization factor will be equal to P (J~ I~)/(i~+i~)(2 1)1(2+1) There are two obvious sources of depolarization: the hyperfine interaction and the coupling to T2g vibrational modes. The hyperfine interaction can be written as I A S with I ~, S I and A~ A7 A, 4GHz for both isotopes 69Ga and 71Ga [2]. It mixes the two radiative states of a given well. In first order of the perturbation one obtains states such as Xy)~M 1)+ Xz~[/ijMi + I) + f3 M1 I)] where M1 is the nuclear spin quantum number. Averaging over the 4 nuclear ‘spin 2 0.08. sublevels one calculates an effective mixing coefficient ~2 ~(AI2E) Taking into account this effect one gets the polarization factor shown in line 2 of table I. If the rhombic term E 0 as it is the case for Ga~in NaCI [3], the mixing of the two radiative states is complete and the highest polarization attainable should be as shown in line 3 of table I. Let us now consider the effect of the coupling to T 25 modes of vibration, It mixes electronic levels having the same spin state but different orbital states: for instance, pumping some highly excited vibrational level of the Yz state will result in populating ground vibrational levels of the Xz and the Zz states. This loss of polarization is characterized by the coefficient a defined in fig. I. The higher in energy one pumps in the A absorption band the larger is a and the smaller the polarization. We have calculated the temperature dependence of the polarization assuming that the relaxation inside a well is a one-phonon process. Then labeling the spin levels i I, 2, 3 in order of increasing energy the transition probability per unit time from level 2 to level I is k2i K(n + I) with the Bose factor ii ll{exp[(D E)/kT] + l} and similarly for the transition rate k5~but with the energy term (D + E) in the exponent. The transition rate from level 3 to level 2 is k52 K’(n + I) with the energy 2E in the Bose factor. All other transition rates are then defined since k~ k3 exp[(E E3)/kTJ. The radiative decay time I/k2 of levels 2 and 3 and the coefficient K were already determined from an 5s analysis ‘ and of Kthe temperature of equations the decaygoverning times [5], k2— l.18xoflOthe populations 0.83 x l0~s dependence Writing the rate the evolution ~.
.
.
Table I
Polarization factor expected for various relaxation and feeding rates
No relaxation Selection rules completely satisfied a /3 0 a 0, /3 small, E 0 a O,E 0/3 1
I I
Relaxation inside and between wells
0 0
2/32
1) I
a0./3 0 a, /3 small
Relaxation inside a well
9a/4
I
I I
la/4 3a/2 2/32
Ia
I
~(I
a 8a/I)
0
Le Si Dang et al/Relaxed excited states of T1-like centers
335
in the usual way one gets a complex expression for the polarization factor. Computer fitting to the experimental points is shown by the solid line in fig. 2. A good fitis obtained for a = 0.19±0.01,p2 = 0.02±0.02,K’ = (0.05 ±0.05)xi05 s p2 seen to be much smaller than the value calculated using the known values of A and E. This discrepancy is not understood presently and needs further study. In summary, the polarization has a complex temperature dependence and only a detailed analysis taking into account the fine structure of the spin states and the hyperfine interaction inside Jahn—Teller wells can explain the experimental results. The main features of the system are the following: there is no tunneling from one Jahn—Teller well to another up to 50 K since the high temperature limit of P is 0. there is some depolarization due to coupling to T~phonons which takes place during the non radiative feeding process since the high temperature limit of P is smaller than the low temperature limit of P is larger than indicating that the radiative spin states are stabilized by the rhombic term E of the spin-Hamiltonian, and are not completely mixed by the hyperfine interaction. —
—
~.
—
References [11 A. Fukuda, S. Makishima, T. Mabuchi and R. Onaka, J. Phys. Chem. Solids 28 (1967) 1763. 121 Le Si Dang, R. Romestain, Y. Merle d’Aubigne and A. Fukuda, Phys. Rev. Lett. 38 (1977) 1539. [3] Le Si Dang, Y. Merle d’Aubigne, R. Romestain and A. Fukuda, Solid State Commun. 26 (1978) 413. [4] P. EdeI, C. Hennies, Y. Merle d’Aubigné, R. Romestain and Y. Twarowski, Phys. Rev. Lett. 28 (1972) 1268. [51 Le Si Dang, R. Romestain, D. Simkin and A. Fukuda, Phys. Rev. B., to be published. [6] S.G. Zazubovich, Opt. Spectry. (USSR) 26 (1969)126.
RELAXED EXCITED STATES OF TI—LIKE CENTERS IN ALKALI HALIDES, POLARIZATION EFFECT OF Ga~CENTER LE SI DANG, Y. MERLE D’AUBIGNE and R. ROMESTAIN Laboratoire de Spectrométrie Physique.* Universifé Scienrifique et Médicale de Grenoble, 38041 Grenoble-Cedex, France
The linear polarization of the AT emission is another clue to the symmetry of the
3T
1, excited states. Besides, it yields quantitative information about dynamical processes such as feeding rates and relaxation or tunneling between the different sublevels ~
1. Introduction Titlike ions in alkali halides have been studied for many years. Measurements of the polarization of the emitted light, when the crystal is excited with polarized light, have shown that the so called A1 emission originates in an orbital triplet with tetragonal Jahn—Teller distortions. Such a study was carried out in KBr:Ga~ at 4.2K by Fukuda et al. [1]. We have measured the temperature dependence of this polarization. The exact level structure of KBr:Ga~being known from EPR [2], it was possible to make a detailed analysis of this temperature dependence. Such quantities as: (i) the populating rates of the various Jahn—Teller wells when exciting with polarized light, (ii) the relaxation times between the various spin sublevels, could be deduced from this analysis. We will briefly recall the model describing the Jahn—Teller effect in the relaxed excited states of Ga~in KBr, then describe the experimental arrangement we used. In the last section we will make the analysis of the temperature dependence of the linear polarization observed. 3T The AT emission from In transitions between the 1~relaxed excited 1Aig originates ground state. the present experiment it is excited by states and the in the A absorption band, ‘Aig~~3Tiu.Optical detection of EPR pumping directly has shown that the 3T 1~excited states are strongly coupled to Eg vibrational modes and this results in static, tetragonal Jahn—Teller distortions [2, 3]. The Jahn—Teller energy is much larger than the spin—orbit coupling constant so that the quantum number J = L + S loses its significance and the level structure is as indicated in fig. 1 (a similar situation would hold for the In~ion but for Tl~the spin—orbit coupling is very large and J keeps its significance). The system lies in one of the Jahn—Teller wells 3T shown in fig. 1. Each of these corresponds to a particular orbital state of the 1~level which we label X, Y and Z. Similarly we *~boratoire associé au C.N.R.S. 331
I e Si Dang ci al/Relaxed excited states of El 1 2 3 1 ~
like cenlers
2)
~(i+~
(1_2~)~2 i—~
2
2
~
x~
John -Teller 1 1 r 1 distortion L100J L°10J Orbital state Y Fig. I. Level structure and optical selection rules of the A
~
[001 Z
1 relaxed excited states of Ga center Wavy arrows indicates the feedings of various spin sublevels for an excitation light polarized along the [1001 direction
label x, y, z the spin triplet states. Dipole—dipole interaction and second order effect of the spin—orbit coupling partially lift the spin degeneracy as shown in fig. I. For a [100] distortion, the singlet Xx state is the lowest and optical transitions from this state to the ground state are strictly forbidden. The doublet states X~ and Xz emit light polarized along the Z and Y directions, respectively. These selection rules are deduced from the fact that the wavefunction (Xy Yx) transforms like the z component of the T1~representation of the Oh group. It is interesting to note that a center which is distorted along a given tetragonal direction emits light polarized in the plane perpendicular to this direction. These selection rules were carefully checked in various cases of strong Jahn—Teller coupling [2,4]. In the case of strong spin—orbit coupling J is a good quantum number and the simple selection rule remains true: the center emits light polarized along the direction of the Jahn—Teller distortion. In NaCl:Ga~the two radiative states, say Xy and Xz for the X distortion, are effectively degenerate [3]. In KBr:Ga they are split by 2E 16GHz which remain small with respect to the zero field splitting D 93.6 GHz between the singlet and the doublet [21. The origin of this orthorhombic term E in the spin-Hamiltonian is not clear: impurity or off-center effect... Since E can he positive or negative, one obtains two non-equivalent centers for each tetragonal Jahn—Teller distortion. 2. Experimental results The measurements made at 4.2 K are in excellent agreement with those of Fukuda et al. [11. We will only describe those made in a simple geometry: both the exciting beam and the collected beam of emitted light propagate along a 10011 direction of the crystal. One defines the polarization factor as P (iii I )/(Iii+ I ), where ~ and I are the intensity of the emitted light with
Le Si Dang et al./ Relaxed excited states of Tl~-likecenters
Temperature
133
(K )
Fig. 2. Temperature dependence of the polarization factor P of the AT emission for polarized excitation at 4.4eV: open circles are experimental points, solid line is theory (see text). Inset shows the variation of the polarization factor when exciting with polarized light in different parts of the A (4.6 eV) and B (4.75 eV) absorption bands at T 4.2 K.
polarization respectively parallel and perpendicular to the polarization of the excitation light. As expected the polarization factor P is maximum when the polarization of the exciting light is along the [100] or [010] directions of the crystal and is zero for the [1101 direction. As shown in the inset of fig. 2 the polarization factor depends on the wavelength of the excitation light. The measurements of the temperature dependence of P are made for low energy excitation as indicated by an arrow in the A absorption band where the effect is the largest. As shown in fig. 2 the effect of temperature on the polarization factor is large. At very low temperatures the relaxation mechanisms are not very efficient so the polarization reflects the feeding rates of the various orbital and spin states. The measurements could not be made above 50 K since most of the emitted light goes into the A~band [5]. It is clear that in this temperature range the polarization factor tends to saturate at a value different from zero. This shows that only relaxation inside a given well takes place because tunneling from one Jahn—Teller well to another would lead to a complete depolarization of the emitted light. Such depolarization is indeed observed for In~in various alkali halides [61for which it is still possible to observe the AT emission at temperatures as high as 300 K.
3. Quantitative analysis of the polarization We will analyse the polarization obtained when pumping with light polarized along the X direction. First let us assume there is no depolarizing effect. Then transitions in the A band are allowed toward the Yz and Zy states. If there were no relaxation, emission would take place from these same states and thus would
114
Le Si Dang ci al/Relaxed excited states of T!’-like centers
be fully X polarized. Relaxation takes place inside a given well and at high temperature will tend to equalize the population of the two radiative levels. Emission occurs now from Yz, Yx, Zy and Zx states which emit X, Z, X and Y polarized light, respectively. Then the polarization factor will be equal to P (J~ I~)/(i~+i~)(2 1)1(2+1) There are two obvious sources of depolarization: the hyperfine interaction and the coupling to T2g vibrational modes. The hyperfine interaction can be written as I A S with I ~, S I and A~ A7 A, 4GHz for both isotopes 69Ga and 71Ga [2]. It mixes the two radiative states of a given well. In first order of the perturbation one obtains states such as Xy)~M 1)+ Xz~[/ijMi + I) + f3 M1 I)] where M1 is the nuclear spin quantum number. Averaging over the 4 nuclear ‘spin 2 0.08. sublevels one calculates an effective mixing coefficient ~2 ~(AI2E) Taking into account this effect one gets the polarization factor shown in line 2 of table I. If the rhombic term E 0 as it is the case for Ga~in NaCI [3], the mixing of the two radiative states is complete and the highest polarization attainable should be as shown in line 3 of table I. Let us now consider the effect of the coupling to T 25 modes of vibration, It mixes electronic levels having the same spin state but different orbital states: for instance, pumping some highly excited vibrational level of the Yz state will result in populating ground vibrational levels of the Xz and the Zz states. This loss of polarization is characterized by the coefficient a defined in fig. I. The higher in energy one pumps in the A absorption band the larger is a and the smaller the polarization. We have calculated the temperature dependence of the polarization assuming that the relaxation inside a well is a one-phonon process. Then labeling the spin levels i I, 2, 3 in order of increasing energy the transition probability per unit time from level 2 to level I is k2i K(n + I) with the Bose factor ii ll{exp[(D E)/kT] + l} and similarly for the transition rate k5~but with the energy term (D + E) in the exponent. The transition rate from level 3 to level 2 is k52 K’(n + I) with the energy 2E in the Bose factor. All other transition rates are then defined since k~ k3 exp[(E E3)/kTJ. The radiative decay time I/k2 of levels 2 and 3 and the coefficient K were already determined from an 5s analysis ‘ and of Kthe temperature of equations the decaygoverning times [5], k2— l.18xoflOthe populations 0.83 x l0~s dependence Writing the rate the evolution ~.
.
.
Table I
Polarization factor expected for various relaxation and feeding rates
No relaxation Selection rules completely satisfied a /3 0 a 0, /3 small, E 0 a O,E 0/3 1
I I
Relaxation inside and between wells
0 0
2/32
1) I
a0./3 0 a, /3 small
Relaxation inside a well
9a/4
I
I I
la/4 3a/2 2/32
Ia
I
~(I
a 8a/I)
0
Le Si Dang et al/Relaxed excited states of T1-like centers
335
in the usual way one gets a complex expression for the polarization factor. Computer fitting to the experimental points is shown by the solid line in fig. 2. A good fitis obtained for a = 0.19±0.01,p2 = 0.02±0.02,K’ = (0.05 ±0.05)xi05 s p2 seen to be much smaller than the value calculated using the known values of A and E. This discrepancy is not understood presently and needs further study. In summary, the polarization has a complex temperature dependence and only a detailed analysis taking into account the fine structure of the spin states and the hyperfine interaction inside Jahn—Teller wells can explain the experimental results. The main features of the system are the following: there is no tunneling from one Jahn—Teller well to another up to 50 K since the high temperature limit of P is 0. there is some depolarization due to coupling to T~phonons which takes place during the non radiative feeding process since the high temperature limit of P is smaller than the low temperature limit of P is larger than indicating that the radiative spin states are stabilized by the rhombic term E of the spin-Hamiltonian, and are not completely mixed by the hyperfine interaction. —
—
~.
—
References [11 A. Fukuda, S. Makishima, T. Mabuchi and R. Onaka, J. Phys. Chem. Solids 28 (1967) 1763. 121 Le Si Dang, R. Romestain, Y. Merle d’Aubigne and A. Fukuda, Phys. Rev. Lett. 38 (1977) 1539. [3] Le Si Dang, Y. Merle d’Aubigne, R. Romestain and A. Fukuda, Solid State Commun. 26 (1978) 413. [4] P. EdeI, C. Hennies, Y. Merle d’Aubigné, R. Romestain and Y. Twarowski, Phys. Rev. Lett. 28 (1972) 1268. [51 Le Si Dang, R. Romestain, D. Simkin and A. Fukuda, Phys. Rev. B., to be published. [6] S.G. Zazubovich, Opt. Spectry. (USSR) 26 (1969)126.